Predicting strengths of concrete-type specimens using hybrid multilayer perceptrons with center-unified particle swarm optimization

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Abstract

This study explores the effectiveness of results obtained by using proposed hybrid multilayer perceptron (HMLP) networks to predict strength in concrete cylinders, reinforced-concrete deep beams, and reinforced-concrete squat walls. Such HMLP networks were designed to incorporate one linear and three high-order layer connections. Of the latter, one, employed only in the first layer connection, was derived from drawings referenced in the literature and two were developed by the author for this study. To calculate appropriate network coefficients, this study designed a center-unified particle swarm optimization (CUPSO) approach, composed of a center particle and global and local variants, which is quite effective for optimization tasks. This study gathered 103, 62, and 62 datasets, respectively, from drawings in three cases reported in the literature. Results, which showed that certain high order HMLP models perform better than their traditional counterpart, evidence the efficacy of proposed HMLP families. Each family, comprising high-order models and a linear counterpart, achieved results that were superior to those attained using traditional MLP networks only.

Introduction

A multilayer perceptrons (MLP) network calculates net value according to associated inputs and multiplicative weights. Without hidden layers, an MLP is able to describe linear problems only. Hidden layers between input–output mapping have been employed to enhance MLP capacity. Various civil engineering problems apply AI approaches to abstract information/knowledge from historical data to predict strength (capacity) (Adhikary and Mutsuyoshi, 2006, Cladera and Mari, 2004, Lee et al., 2003, Mansour et al., 2004, Oh et al., 1999, Oreta, 2004, Sanad and Saka, 2001, Yeh, 2006).

The high-order neural network (HONN) was developed about 1990. Its nonlinear combination of inputs (Zurada, 1992) allows such networks to capture high-order correlations easily and achieve effective nonlinear mapping. As HONNs use high-order correlations, they may perform better than linear NNs. Sigma-pi and ExpoNet are two types of HONN models. To combine the above two models, Abdelbar and Tagliarini (1996) developed the HONEST model, which created an effective hybrid of sigma-pi and ExpoNet. The original HONEST was architecture of three layers, which employed both a multiplier operator and exponent terms for the first layer connection and used traditional connection for the second/last connection.

There are various high-order networks and they have been widely applied in various research domains, especially for pattern recognition and function approximation (Artyomov and Yadid-Pecht, 2005, Foresti and Dolso, 2004, Rovithakis et al., 2004, Wang and Lin, 1995). Such references have proofed HONN models as a powerful approach to artificial intelligence (AI). In past studies, HONN models have usually been modified for particular problems with simplified topologies (only one high-order connection typically used and constrained for a particular connection).

Previous studies by the author focused on derived error back-propagation algorithms for high-order neural networks in which the high-order connection is not constrained to particular connections (Tsai, 2009). Furthermore, new high-order MLP layer connectors, all derivative models and linear counterparts defined as hybrid multilayer perceptrons (HMLP), were developed and studied by the author. Half of these proposed HMLP models addressed various problems successfully and were designated as valid HMLP models, which the author employed in this study to predict the strength capacity of various concrete-type specimens.

Concrete is a complex material in wide use due to its strong capacity to withstand compression. However, identifying the specific mechanics of concrete and its derivatives is a difficult task. Predicting strength capacity is made more difficult still due to the reliance of such on identified mechanics. Using an AI approach represents an alternative method of predicting strength. Although the AI solution cannot replace specific equations, it provides strength references that provide typically greater levels of accuracy.

The main purpose of this paper was to apply valid HMLP models to predict the specimen strength of concrete and its derivatives. Results focused on the performance of proposed high-order HMLP model in comparison with that of their linear counterpart. There are many HMLP models await to be performed. The use of optimization techniques was an alternative to deriving learning equations. Swarm intelligence represents a relatively new category of stochastic, population-based optimization algorithms. The particle swarm optimization (PSO) was introduced by Eberhart and Kennedy, 1995a, Eberhart and Kennedy, 1995b. Derivative approaches, including unified PSO (Parsopoulos & Vrahatis, 2004) and center PSO (Liu, Qin, Shi, & Lu, 2007), have since been proposed. Significant parameter settings have also been previously studied and proposed (Parsopoulos & Vrahatis, 2007). With the exception of function optimization, PSO has been applied for NN learning (Liu et al., 2007). Zhang, Zhang, Lok, and Lyu (2007) also hybridized particle swarm optimization (PSO) and error back-propagation algorithms for feedforward NN training. The author integrated the unified PSO and center PSO into a “center-unified” PSO (CUPSO) for use in this study.

The remaining sections of this paper include Section 2: proposed HMLP models; Section 3: CUPSO approaches; Section 4: predicting specimen strengths of concrete cylinders, reinforced-concrete deep beams, and reinforced-concrete squat walls, and Section 5: Conclusions.

Section snippets

Hybrid multilayer perceptrons

The proposed hybrid multilayer perceptrons (HMLP) network is activated with four kinds of layer connection candidates that include a traditional linear connection and three high-order remainders. Connection functionalities for two adjacent layers follow scenarios described below (refer to Fig. 1):yi=fnetiCT,CT{1,2,3,4}f(x)=11+e-xneti1=jwijxj+1wi0neti2=jxjpij1pi0neti3=jwijxjpij+wi01pi0neti4=jwijxjpijwi01pi0where i is the corresponding output neurons and j represents the input unit. A

Standard PSO

Particle swarm optimization, an optimization tool developed by Eberhart and Kennedy, 1995a, Eberhart and Kennedy, 1995b was inspired by the flocking behavior of birds. It is a swarm intelligence algorithm that is typically employed in numerical optimization problems and which has gained popularity in recent years due to its efficiency and effectiveness addressing problems in the realms of science and engineering. Similar to the genetic algorithm, PSO is based on a population that is initialized

Predicting strengths of concrete-type specimens

Concrete, a material with a complicated composition, is used widely in construction engineering. Reinforced-concrete components comprise two different materials, namely concrete (providing compression resistance) and steel (providing tension resistance). Concrete in various formats can service the capacity needs of a wide range of construction applications. Capacities can be calculated with a significant mechanism and should be based on experimental testing results. Unfortunately, as various

Conclusions

This study introduced three high-order connectors to a traditional multilayer perceptron (MLP) network. Four layer connectors, including three high-order ones and the traditional linear one, were used to construct the proposed hybrid multilayer perceptron (HMLP) families for this study. This paper applied valid HMLP models with one hidden layer, i.e. those in the HMLP2 family, to three strength learning cases (concrete cylinders, deep beams, and squat walls) in order to predict specimen

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